In this article, the lubrication of a long porous slider in which the fluid is injected into the porous bottom is considered. The similarity transformations reduce the governing problem of Navier-Stokes equations to coupled nonlinear ordinary differential equations which are solved by HAM. Solutions are obtained for much larger values of Reynolds number compared to analytical and numerical methods. The results comprise good agreement between approximate and numerical solutions. HAM gives rapid convergent series solutions which show that this method is efficient, accurate and has advantages over other methods. Further, homotopy-pade’ technique is used to accelerate the convergence of series solution.
This paper presents Dirichlet series and approximate analytical solutions of magnetohydrodynamic (MHD) flow due to a suction / blowing caused by boundary layer of an incompressible viscous flow. The governing nonlinear partial differential equations of momentum equations are reduced into a set of nonlinear ordinary differential equations (ODE) by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel mathematical tools for their analysis. We use elegant fast converging Dirichlet series and approximate analytical solutions (method of stretching of variables) of these nonlinear differential equations. These methods have advantages over pure numerical methods for obtaining derived quantities accurately for various values of the parameters involved at a stretch and also they are valid in much larger parameter domains as compared with DTM-Padé and classical numerical schemes.
Graph energy and Domination in graphs are most studied areas of graph theory. In this paper we made an attempt to connect these two areas of graph theory by introducing c-dominating energy of a graph G. First, we show the chemical applications of c-dominating energy with the help of well known statistical tools. Next, we obtain mathematical properties of c-dominating energy. Finally, we characterize trees, unicyclic graphs, cubic and block graphs with equal dominating and c-dominating energy.
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